IJPAM: Volume 95, No. 3 (2014)

CONVEXITY AND TWO PIECE PROPERTY IN $S^n$

M. Beltgy$^1$, S. Shenawy$^2$, A. Elsharkawy$^3$
$^1$Mathematics Department
Faculty of Science
Tanta University
Tanta, EGYPT
$^2$Modern Academy for Engineering and Technology in Maadi
Maadi, EGYPT
$^3$Faculty of Science
Tanta University
Tanta, EGYPT


Abstract. A subset $A$ of $S^n$, $n\geq2$, has spherical two piece property if any hypersphere cuts $A$ into at most two pieces. A subset $A$ of $S^n$ has totally geodesic two piece property if any totally geodesic hypersurface in $S^n$, $n\geq2$, cuts $A$ into at most two pieces. In this article we study some geometric properties of subsets in $S^{n}$-as a manifold with focal points and these types of two piece property in $S^n$.

Received: March 12, 2014

AMS Subject Classification: 53C42, 52A05

Key Words and Phrases: sphere $S^n$, convex sets, supporting totally geodesic hypersurface, spherical two piece property, totally geodesic two piece property and Tight immersions

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DOI: 10.12732/ijpam.v95i3.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 95
Issue: 3
Pages: 347 - 356


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